Chapter 2 DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS

1 45 Chapter 2 DOSIMETRIC PRINCIPLES, QUANTITIES AND UNITSJ. P. S E U N T J E N SDepartment of Medical Physics,McGill University Health Centre,Montreal, Quebec, CanadaW. S T RY D O MDepartment of Medical Physics,Medical University of Southern Africa,Pretoria, South SHORTTD ivision of Human Health,International Atomic Energy Agency, INTRODUCTIONR adiation measurements and investigations of radiation effects require various specifications of the radiation field at the point of interest. Radiation dosimetry deals with methods for a quantitative determination of energy deposited in a given medium by directly or indirectly ionizing radiations.

2 A number of QUANTITIES and UNITS have been defined for describing the radiation beam, and the most commonly used DOSIMETRIC QUANTITIES and their UNITS are defined below. A simplified discussion of cavity theory, the theory that deals with calculating the response of a dosimeter in a medium, is also PHOTON FLUENCE AND ENERGY FLUENCEThe following QUANTITIES are used to describe a monoenergetic ionizing radiation beam: particle fluence, energy fluence, particle fluence rate and energy fluence rate. These QUANTITIES are usually used to describe photon beams and may also be used in describing charged particle 246 The particle fluence F is the quotient dN by dA, where dN is the number of particles incident on a sphere of cross-sectional area dA:( )The unit of particle fluence is m 2.

3 The use of a sphere of cross-sectional area dA expresses in the simplest manner the fact that one considers an area dA perpendicular to the direction of each particle and hence that particle fluence is independent of the incident angle of the radiation. Planar particle fluence is the number of particles crossing a plane per unit area and hence depends on the angle of incidence of the particle beam. The energy fluence Y is the quotient of dE by dA, where dE is the radiant energy incident on a sphere of cross-sectional area dA:( )The unit of energy fluence is J/m2.

4 Energy fluence can be calculated from particle fluence by using the following relation:( )where E is the energy of the particle and dN represents the number of particles with energy all realistic photon or particle beams are polyenergetic, and the above defined concepts need to be applied to such beams. The concepts of particle fluence spectrum and energy fluence spectrum replace the particle fluence and energy fluence, respectively. They are defined respectively as:( )and( )where FE(E) and YE(E) are shorthand notations for the particle fluence spectrum and the energy fluence spectrum differential in energy E, respec-tively.

5 Figure shows a photon fluence and an energy fluence spectrum generated by an orthovoltage X ray unit with a kVp value of 250 kV and an F=ddNAY=ddEAYF==ddNAEEFFEEEE()() ddYYFEEEEEEE()()() =ddddDOSIMETRIC PRINCIPLES, QUANTITIES AND UNITS47added filtration of 1 mm Al and mm Cu (target material: W; inherent filtration: 2 mm Be). The two spikes superimposed on the continuous bremsstrahlung spectrum represent the Ka and the Kb characteristic X ray lines produced in the tungsten particle fluence rate F is the quotient of dF by dt, where dF is the increment of the fluence in time interval dt:( )with UNITS of m 2 s energy fluence rate (also referred to as intensity) is the quotient of dY by dt, where dY is the increment of the energy fluence in the time interval dt.

6 ( )The unit of energy fluence rate is W/m2 or J m 2 s fluence spectrumEnergy fluence spectrum50 100 150 200 250 Energy (keV) (arbitrary UNITS )FIG. Photon fluence and energy fluence spectra at 1 m from the target of an X ray machine with a tube potential of 250 kV and added filtration of 1 mm Al and mm Cu (target material: W; inherent filtration: 2 mm Be). FF=ddt YY=ddtCHAPTER KERMAK erma is an acronym for kinetic energy released per unit mass. It is a non-stochastic quantity applicable to indirectly ionizing radiations such as photons and neutrons.

7 It quantifies the average amount of energy transferred from indirectly ionizing radiation to directly ionizing radiation without concern as to what happens after this transfer. In the discussion that follows we will limit ourselves to energy of photons is imparted to matter in a two stage process. In the first stage, the photon radiation transfers energy to the secondary charged particles (electrons) through various photon interactions (the photoelectric effect, the Compton effect, pair production, etc.). In the second stage, the charged particle transfers energy to the medium through atomic excitations and ionizations.

8 In this context, the kerma is defined as the mean energy transferred from the indirectly ionizing radiation to charged particles (electrons) in the medium per unit mass dm: ( )The unit of kerma is joule per kilogram (J/kg). The name for the unit of kerma is the gray (Gy), where 1 Gy = 1 CEMACema is the acronym for converted energy per unit mass. It is a non-stochastic quantity applicable to directly ionizing radiations such as electrons and protons. The cema C is the quotient of dEc by dm, where dEc is the energy lost by charged particles, except secondary electrons, in collisions in a mass dmof a material:( )The unit of cema is joule per kilogram (J/kg).

9 The name for the unit of cema is the gray (Gy).EdtrKEm=ddtrCEm=ddcDOSIMETRIC PRINCIPLES, QUANTITIES AND ABSORBED DOSEA bsorbed dose is a non-stochastic quantity applicable to both indirectly and directly ionizing radiations. For indirectly ionizing radiations, energy is imparted to matter in a two step process. In the first step (resulting in kerma), the indirectly ionizing radiation transfers energy as kinetic energy to secondary charged particles. In the second step, these charged particles transfer some of their kinetic energy to the medium (resulting in absorbed dose) and lose some of their energy in the form of radiative losses (bremsstrahlung, annihilation in flight).

10 The absorbed dose is related to the stochastic quantity energy imparted. The absorbed dose is defined as the mean energy e imparted by ionizing radiation to matter of mass m in a finite volume V by: ( )The energy imparted e is the sum of all the energy entering the volume of interest minus all the energy leaving the volume, taking into account any mass energy conversion within the volume. Pair production, for example, decreases the energy by MeV, while electron positron annihilation increases the energy by the same that because electrons travel in the medium and deposit energy along their tracks, this absorption of energy does not take place at the same location as the transfer of energy described by kerma.